Sample size for a mean confidence interval using a planning value from a prior study

Computes the sample size required to estimate a population mean with desired confidence interval precision in applications where an estimated variance from a prior study is available. The actual confidence interval width in the planned study will depend on the value of the estimated variance in the planned study. An estimated variance from a prior study can be used to compute an upper prediction limit for the estimated variance in the planned study. The upper prediction limit is then used as the variance planning value. Using a larger confidence level (1 - alpha2) for the upper prediction limit will increase the probability that the width of of the confidence interval for the population mean in the planned study will be less than or equal to the desired width.

This sample size approach assumes that the population variance in the prior study is very similar to the population variance in the planned study. However, this type of prior information is typically not available, and the researcher must use expert opinion to guess the value of the variance that will be observed in the planned study. The size.ci.mean function uses a variance planning value that is based on expert opinion regarding the likely value of the variance estimate that will be observed in the planned study.

Usage

size.ci.mean.prior(alpha1, alpha2, var0, n0, w)

Arguments

alpha1

alpha level for 1-alpha1 confidence in the planned study

alpha2

alpha level for the 1-alpha2 prediction interval

var0

estimated variance in prior study

n0

sample size in prior study

w

desired confidence interval width

Value

Returns the required sample size

Examples

size.ci.mean.prior(.05, .10, 26.4, 25, 4)
#>  Sample size
#>           44

# Should return:
# Sample size
#          44